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Transverse electron focusing in a two-dimensional electron gas is investigated experimentally and theoretically for the first time. A split Schottky gate on top of a GaAs-AlₗGa₁-ₗAs heterostructure defines two point contacts of variable width, which are used as injector and collector of ballistic electrons. As evidenced by their quantized conductance, these are quantum point contacts with a width comparable to the Fermi wavelength. At low magnetic fields, skipping orbits at the electron-gas boundary are directly observed, thereby establishing that boundary scattering is highly specular. Large additional oscillatory structure in the focusing spectra is observed at low temperatures and for small point-contact size. This new phenomenon is interpreted in terms of interference of coherently excited magnetic edge states in a two-dimensional electron gas. A theory for this effect is given, and the relation with nonlocal resistance measurements in quantum ballistic transport is discussed. It is pointed out, and experimentally demonstrated, that four-terminal transport measurements in the electron-focusing geometry constitute a determination of either a generalized longitudinal resistance or a Hall resistance. At high magnetic fields the electron-focusing peaks are suppressed, and a transition is observed to the quantum Hall regime. The anomalous quantum Hall effect in this geometry is discussed in light of a four-terminal resistance formula.
Houten et al. (Sat,) studied this question.